Best Known (138−10, 138, s)-Nets in Base 2
(138−10, 138, 2796200)-Net over F2 — Constructive and digital
Digital (128, 138, 2796200)-net over F2, using
- net defined by OOA [i] based on linear OOA(2138, 2796200, F2, 14, 10) (dual of [(2796200, 14), 39146662, 11]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(2138, 8388601, F2, 2, 10) (dual of [(8388601, 2), 16777064, 11]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2138, 8388602, F2, 2, 10) (dual of [(8388602, 2), 16777066, 11]-NRT-code), using
- 1 step truncation [i] based on linear OOA(2139, large, F2, 2, 11), using
- discarding factors / shortening the dual code based on linear OOA(2138, 8388602, F2, 2, 10) (dual of [(8388602, 2), 16777066, 11]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(2138, 8388601, F2, 2, 10) (dual of [(8388601, 2), 16777064, 11]-NRT-code), using
(138−10, 138, 4194305)-Net over F2 — Digital
Digital (128, 138, 4194305)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2138, 4194305, F2, 3, 10) (dual of [(4194305, 3), 12582777, 11]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(25, 3, F2, 3, 5) (dual of [(3, 3), 4, 6]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;4,2) [i]
- linear OOA(2133, 4194302, F2, 3, 10) (dual of [(4194302, 3), 12582773, 11]-NRT-code), using
- 1 step truncation [i] based on linear OOA(2134, 4194303, F2, 3, 11) (dual of [(4194303, 3), 12582775, 12]-NRT-code), using
- linear OOA(25, 3, F2, 3, 5) (dual of [(3, 3), 4, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
(138−10, 138, large)-Net in Base 2 — Upper bound on s
There is no (128, 138, large)-net in base 2, because
- 8 times m-reduction [i] would yield (128, 130, large)-net in base 2, but